STUDENT NAME & ID : ARJUN KC(8773456)¶

In [1]:
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import seaborn as sns
import plotly
import plotly.express as px
import sklearn
from sklearn import datasets
plotly.offline.init_notebook_mode()
sns.set_style("whitegrid")

Loading the dataset of Diabetics from Sklearn¶

In [4]:
diabtics = datasets.load_diabetes()
In [5]:
diabtics
Out[5]:
{'data': array([[ 0.03807591,  0.05068012,  0.06169621, ..., -0.00259226,
          0.01990749, -0.01764613],
        [-0.00188202, -0.04464164, -0.05147406, ..., -0.03949338,
         -0.06833155, -0.09220405],
        [ 0.08529891,  0.05068012,  0.04445121, ..., -0.00259226,
          0.00286131, -0.02593034],
        ...,
        [ 0.04170844,  0.05068012, -0.01590626, ..., -0.01107952,
         -0.04688253,  0.01549073],
        [-0.04547248, -0.04464164,  0.03906215, ...,  0.02655962,
          0.04452873, -0.02593034],
        [-0.04547248, -0.04464164, -0.0730303 , ..., -0.03949338,
         -0.00422151,  0.00306441]]),
 'target': array([151.,  75., 141., 206., 135.,  97., 138.,  63., 110., 310., 101.,
         69., 179., 185., 118., 171., 166., 144.,  97., 168.,  68.,  49.,
         68., 245., 184., 202., 137.,  85., 131., 283., 129.,  59., 341.,
         87.,  65., 102., 265., 276., 252.,  90., 100.,  55.,  61.,  92.,
        259.,  53., 190., 142.,  75., 142., 155., 225.,  59., 104., 182.,
        128.,  52.,  37., 170., 170.,  61., 144.,  52., 128.,  71., 163.,
        150.,  97., 160., 178.,  48., 270., 202., 111.,  85.,  42., 170.,
        200., 252., 113., 143.,  51.,  52., 210.,  65., 141.,  55., 134.,
         42., 111.,  98., 164.,  48.,  96.,  90., 162., 150., 279.,  92.,
         83., 128., 102., 302., 198.,  95.,  53., 134., 144., 232.,  81.,
        104.,  59., 246., 297., 258., 229., 275., 281., 179., 200., 200.,
        173., 180.,  84., 121., 161.,  99., 109., 115., 268., 274., 158.,
        107.,  83., 103., 272.,  85., 280., 336., 281., 118., 317., 235.,
         60., 174., 259., 178., 128.,  96., 126., 288.,  88., 292.,  71.,
        197., 186.,  25.,  84.,  96., 195.,  53., 217., 172., 131., 214.,
         59.,  70., 220., 268., 152.,  47.,  74., 295., 101., 151., 127.,
        237., 225.,  81., 151., 107.,  64., 138., 185., 265., 101., 137.,
        143., 141.,  79., 292., 178.,  91., 116.,  86., 122.,  72., 129.,
        142.,  90., 158.,  39., 196., 222., 277.,  99., 196., 202., 155.,
         77., 191.,  70.,  73.,  49.,  65., 263., 248., 296., 214., 185.,
         78.,  93., 252., 150.,  77., 208.,  77., 108., 160.,  53., 220.,
        154., 259.,  90., 246., 124.,  67.,  72., 257., 262., 275., 177.,
         71.,  47., 187., 125.,  78.,  51., 258., 215., 303., 243.,  91.,
        150., 310., 153., 346.,  63.,  89.,  50.,  39., 103., 308., 116.,
        145.,  74.,  45., 115., 264.,  87., 202., 127., 182., 241.,  66.,
         94., 283.,  64., 102., 200., 265.,  94., 230., 181., 156., 233.,
         60., 219.,  80.,  68., 332., 248.,  84., 200.,  55.,  85.,  89.,
         31., 129.,  83., 275.,  65., 198., 236., 253., 124.,  44., 172.,
        114., 142., 109., 180., 144., 163., 147.,  97., 220., 190., 109.,
        191., 122., 230., 242., 248., 249., 192., 131., 237.,  78., 135.,
        244., 199., 270., 164.,  72.,  96., 306.,  91., 214.,  95., 216.,
        263., 178., 113., 200., 139., 139.,  88., 148.,  88., 243.,  71.,
         77., 109., 272.,  60.,  54., 221.,  90., 311., 281., 182., 321.,
         58., 262., 206., 233., 242., 123., 167.,  63., 197.,  71., 168.,
        140., 217., 121., 235., 245.,  40.,  52., 104., 132.,  88.,  69.,
        219.,  72., 201., 110.,  51., 277.,  63., 118.,  69., 273., 258.,
         43., 198., 242., 232., 175.,  93., 168., 275., 293., 281.,  72.,
        140., 189., 181., 209., 136., 261., 113., 131., 174., 257.,  55.,
         84.,  42., 146., 212., 233.,  91., 111., 152., 120.,  67., 310.,
         94., 183.,  66., 173.,  72.,  49.,  64.,  48., 178., 104., 132.,
        220.,  57.]),
 'frame': None,
 'DESCR': '.. _diabetes_dataset:\n\nDiabetes dataset\n----------------\n\nTen baseline variables, age, sex, body mass index, average blood\npressure, and six blood serum measurements were obtained for each of n =\n442 diabetes patients, as well as the response of interest, a\nquantitative measure of disease progression one year after baseline.\n\n**Data Set Characteristics:**\n\n  :Number of Instances: 442\n\n  :Number of Attributes: First 10 columns are numeric predictive values\n\n  :Target: Column 11 is a quantitative measure of disease progression one year after baseline\n\n  :Attribute Information:\n      - age     age in years\n      - sex\n      - bmi     body mass index\n      - bp      average blood pressure\n      - s1      tc, total serum cholesterol\n      - s2      ldl, low-density lipoproteins\n      - s3      hdl, high-density lipoproteins\n      - s4      tch, total cholesterol / HDL\n      - s5      ltg, possibly log of serum triglycerides level\n      - s6      glu, blood sugar level\n\nNote: Each of these 10 feature variables have been mean centered and scaled by the standard deviation times the square root of `n_samples` (i.e. the sum of squares of each column totals 1).\n\nSource URL:\nhttps://www4.stat.ncsu.edu/~boos/var.select/diabetes.html\n\nFor more information see:\nBradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani (2004) "Least Angle Regression," Annals of Statistics (with discussion), 407-499.\n(https://web.stanford.edu/~hastie/Papers/LARS/LeastAngle_2002.pdf)\n',
 'feature_names': ['age',
  'sex',
  'bmi',
  'bp',
  's1',
  's2',
  's3',
  's4',
  's5',
  's6'],
 'data_filename': 'diabetes_data_raw.csv.gz',
 'target_filename': 'diabetes_target.csv.gz',
 'data_module': 'sklearn.datasets.data'}
In [6]:
list(diabtics)
Out[6]:
['data',
 'target',
 'frame',
 'DESCR',
 'feature_names',
 'data_filename',
 'target_filename',
 'data_module']
In [7]:
print(diabtics["DESCR"])

.. _diabetes_dataset:

Diabetes dataset
----------------

Ten baseline variables, age, sex, body mass index, average blood
pressure, and six blood serum measurements were obtained for each of n =
442 diabetes patients, as well as the response of interest, a
quantitative measure of disease progression one year after baseline.

**Data Set Characteristics:**

  :Number of Instances: 442

  :Number of Attributes: First 10 columns are numeric predictive values

  :Target: Column 11 is a quantitative measure of disease progression one year after baseline

  :Attribute Information:
      - age     age in years
      - sex
      - bmi     body mass index
      - bp      average blood pressure
      - s1      tc, total serum cholesterol
      - s2      ldl, low-density lipoproteins
      - s3      hdl, high-density lipoproteins
      - s4      tch, total cholesterol / HDL
      - s5      ltg, possibly log of serum triglycerides level
      - s6      glu, blood sugar level

Note: Each of these 10 feature variables have been mean centered and scaled by the standard deviation times the square root of `n_samples` (i.e. the sum of squares of each column totals 1).

Source URL:
https://www4.stat.ncsu.edu/~boos/var.select/diabetes.html

For more information see:
Bradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani (2004) "Least Angle Regression," Annals of Statistics (with discussion), 407-499.
(https://web.stanford.edu/~hastie/Papers/LARS/LeastAngle_2002.pdf)
In [8]:
x = diabtics["data"]
print(x)
print(x.shape)

[[ 0.03807591  0.05068012  0.06169621 ... -0.00259226  0.01990749
  -0.01764613]
 [-0.00188202 -0.04464164 -0.05147406 ... -0.03949338 -0.06833155
  -0.09220405]
 [ 0.08529891  0.05068012  0.04445121 ... -0.00259226  0.00286131
  -0.02593034]
 ...
 [ 0.04170844  0.05068012 -0.01590626 ... -0.01107952 -0.04688253
   0.01549073]
 [-0.04547248 -0.04464164  0.03906215 ...  0.02655962  0.04452873
  -0.02593034]
 [-0.04547248 -0.04464164 -0.0730303  ... -0.03949338 -0.00422151
   0.00306441]]
(442, 10)
In [9]:
y = diabtics["target"]
print(y)
print(y.shape)

[151.  75. 141. 206. 135.  97. 138.  63. 110. 310. 101.  69. 179. 185.
 118. 171. 166. 144.  97. 168.  68.  49.  68. 245. 184. 202. 137.  85.
 131. 283. 129.  59. 341.  87.  65. 102. 265. 276. 252.  90. 100.  55.
  61.  92. 259.  53. 190. 142.  75. 142. 155. 225.  59. 104. 182. 128.
  52.  37. 170. 170.  61. 144.  52. 128.  71. 163. 150.  97. 160. 178.
  48. 270. 202. 111.  85.  42. 170. 200. 252. 113. 143.  51.  52. 210.
  65. 141.  55. 134.  42. 111.  98. 164.  48.  96.  90. 162. 150. 279.
  92.  83. 128. 102. 302. 198.  95.  53. 134. 144. 232.  81. 104.  59.
 246. 297. 258. 229. 275. 281. 179. 200. 200. 173. 180.  84. 121. 161.
  99. 109. 115. 268. 274. 158. 107.  83. 103. 272.  85. 280. 336. 281.
 118. 317. 235.  60. 174. 259. 178. 128.  96. 126. 288.  88. 292.  71.
 197. 186.  25.  84.  96. 195.  53. 217. 172. 131. 214.  59.  70. 220.
 268. 152.  47.  74. 295. 101. 151. 127. 237. 225.  81. 151. 107.  64.
 138. 185. 265. 101. 137. 143. 141.  79. 292. 178.  91. 116.  86. 122.
  72. 129. 142.  90. 158.  39. 196. 222. 277.  99. 196. 202. 155.  77.
 191.  70.  73.  49.  65. 263. 248. 296. 214. 185.  78.  93. 252. 150.
  77. 208.  77. 108. 160.  53. 220. 154. 259.  90. 246. 124.  67.  72.
 257. 262. 275. 177.  71.  47. 187. 125.  78.  51. 258. 215. 303. 243.
  91. 150. 310. 153. 346.  63.  89.  50.  39. 103. 308. 116. 145.  74.
  45. 115. 264.  87. 202. 127. 182. 241.  66.  94. 283.  64. 102. 200.
 265.  94. 230. 181. 156. 233.  60. 219.  80.  68. 332. 248.  84. 200.
  55.  85.  89.  31. 129.  83. 275.  65. 198. 236. 253. 124.  44. 172.
 114. 142. 109. 180. 144. 163. 147.  97. 220. 190. 109. 191. 122. 230.
 242. 248. 249. 192. 131. 237.  78. 135. 244. 199. 270. 164.  72.  96.
 306.  91. 214.  95. 216. 263. 178. 113. 200. 139. 139.  88. 148.  88.
 243.  71.  77. 109. 272.  60.  54. 221.  90. 311. 281. 182. 321.  58.
 262. 206. 233. 242. 123. 167.  63. 197.  71. 168. 140. 217. 121. 235.
 245.  40.  52. 104. 132.  88.  69. 219.  72. 201. 110.  51. 277.  63.
 118.  69. 273. 258.  43. 198. 242. 232. 175.  93. 168. 275. 293. 281.
  72. 140. 189. 181. 209. 136. 261. 113. 131. 174. 257.  55.  84.  42.
 146. 212. 233.  91. 111. 152. 120.  67. 310.  94. 183.  66. 173.  72.
  49.  64.  48. 178. 104. 132. 220.  57.]
(442,)
In [10]:
df1 = diabtics["feature_names"]
print(df1)
len(df1)

['age', 'sex', 'bmi', 'bp', 's1', 's2', 's3', 's4', 's5', 's6']
Out[10]:
10

Creating the dataframe¶

In [11]:
df =pd.DataFrame(x, columns= df1)
df
Out[11]:
age sex bmi bp s1 s2 s3 s4 s5 s6
0 0.038076 0.050680 0.061696 0.021872 -0.044223 -0.034821 -0.043401 -0.002592 0.019907 -0.017646
1 -0.001882 -0.044642 -0.051474 -0.026328 -0.008449 -0.019163 0.074412 -0.039493 -0.068332 -0.092204
2 0.085299 0.050680 0.044451 -0.005670 -0.045599 -0.034194 -0.032356 -0.002592 0.002861 -0.025930
3 -0.089063 -0.044642 -0.011595 -0.036656 0.012191 0.024991 -0.036038 0.034309 0.022688 -0.009362
4 0.005383 -0.044642 -0.036385 0.021872 0.003935 0.015596 0.008142 -0.002592 -0.031988 -0.046641
... ... ... ... ... ... ... ... ... ... ...
437 0.041708 0.050680 0.019662 0.059744 -0.005697 -0.002566 -0.028674 -0.002592 0.031193 0.007207
438 -0.005515 0.050680 -0.015906 -0.067642 0.049341 0.079165 -0.028674 0.034309 -0.018114 0.044485
439 0.041708 0.050680 -0.015906 0.017293 -0.037344 -0.013840 -0.024993 -0.011080 -0.046883 0.015491
440 -0.045472 -0.044642 0.039062 0.001215 0.016318 0.015283 -0.028674 0.026560 0.044529 -0.025930
441 -0.045472 -0.044642 -0.073030 -0.081413 0.083740 0.027809 0.173816 -0.039493 -0.004222 0.003064

442 rows × 10 columns

Adding one more feature "disease_progression" with its target data to the dataframe¶

In [12]:
df["disease_progression"] = diabtics["target"]
df
Out[12]:
age sex bmi bp s1 s2 s3 s4 s5 s6 disease_progression
0 0.038076 0.050680 0.061696 0.021872 -0.044223 -0.034821 -0.043401 -0.002592 0.019907 -0.017646 151.0
1 -0.001882 -0.044642 -0.051474 -0.026328 -0.008449 -0.019163 0.074412 -0.039493 -0.068332 -0.092204 75.0
2 0.085299 0.050680 0.044451 -0.005670 -0.045599 -0.034194 -0.032356 -0.002592 0.002861 -0.025930 141.0
3 -0.089063 -0.044642 -0.011595 -0.036656 0.012191 0.024991 -0.036038 0.034309 0.022688 -0.009362 206.0
4 0.005383 -0.044642 -0.036385 0.021872 0.003935 0.015596 0.008142 -0.002592 -0.031988 -0.046641 135.0
... ... ... ... ... ... ... ... ... ... ... ...
437 0.041708 0.050680 0.019662 0.059744 -0.005697 -0.002566 -0.028674 -0.002592 0.031193 0.007207 178.0
438 -0.005515 0.050680 -0.015906 -0.067642 0.049341 0.079165 -0.028674 0.034309 -0.018114 0.044485 104.0
439 0.041708 0.050680 -0.015906 0.017293 -0.037344 -0.013840 -0.024993 -0.011080 -0.046883 0.015491 132.0
440 -0.045472 -0.044642 0.039062 0.001215 0.016318 0.015283 -0.028674 0.026560 0.044529 -0.025930 220.0
441 -0.045472 -0.044642 -0.073030 -0.081413 0.083740 0.027809 0.173816 -0.039493 -0.004222 0.003064 57.0

442 rows × 11 columns

In [13]:
df.shape
Out[13]:
(442, 11)

Some general Statitical data¶

In [14]:
df.describe()
Out[14]:
age sex bmi bp s1 s2 s3 s4 s5 s6 disease_progression
count 4.420000e+02 4.420000e+02 4.420000e+02 4.420000e+02 4.420000e+02 4.420000e+02 4.420000e+02 4.420000e+02 4.420000e+02 4.420000e+02 442.000000
mean -2.511817e-19 1.230790e-17 -2.245564e-16 -4.797570e-17 -1.381499e-17 3.918434e-17 -5.777179e-18 -9.042540e-18 9.293722e-17 1.130318e-17 152.133484
std 4.761905e-02 4.761905e-02 4.761905e-02 4.761905e-02 4.761905e-02 4.761905e-02 4.761905e-02 4.761905e-02 4.761905e-02 4.761905e-02 77.093005
min -1.072256e-01 -4.464164e-02 -9.027530e-02 -1.123988e-01 -1.267807e-01 -1.156131e-01 -1.023071e-01 -7.639450e-02 -1.260971e-01 -1.377672e-01 25.000000
25% -3.729927e-02 -4.464164e-02 -3.422907e-02 -3.665608e-02 -3.424784e-02 -3.035840e-02 -3.511716e-02 -3.949338e-02 -3.324559e-02 -3.317903e-02 87.000000
50% 5.383060e-03 -4.464164e-02 -7.283766e-03 -5.670422e-03 -4.320866e-03 -3.819065e-03 -6.584468e-03 -2.592262e-03 -1.947171e-03 -1.077698e-03 140.500000
75% 3.807591e-02 5.068012e-02 3.124802e-02 3.564379e-02 2.835801e-02 2.984439e-02 2.931150e-02 3.430886e-02 3.243232e-02 2.791705e-02 211.500000
max 1.107267e-01 5.068012e-02 1.705552e-01 1.320436e-01 1.539137e-01 1.987880e-01 1.811791e-01 1.852344e-01 1.335973e-01 1.356118e-01 346.000000

let's see the datatype¶

In [15]:
df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 442 entries, 0 to 441
Data columns (total 11 columns):
 #   Column               Non-Null Count  Dtype  
---  ------               --------------  -----  
 0   age                  442 non-null    float64
 1   sex                  442 non-null    float64
 2   bmi                  442 non-null    float64
 3   bp                   442 non-null    float64
 4   s1                   442 non-null    float64
 5   s2                   442 non-null    float64
 6   s3                   442 non-null    float64
 7   s4                   442 non-null    float64
 8   s5                   442 non-null    float64
 9   s6                   442 non-null    float64
 10  disease_progression  442 non-null    float64
dtypes: float64(11)
memory usage: 38.1 KB

Let's see for the null value or missing value¶

In [16]:
df.isnull().sum()
Out[16]:
age                    0
sex                    0
bmi                    0
bp                     0
s1                     0
s2                     0
s3                     0
s4                     0
s5                     0
s6                     0
disease_progression    0
dtype: int64

Lets do some EDA¶

In [17]:
plt.figure(figsize=(8,8))
arj = sns.heatmap(df.corr(),annot= True)
In [18]:
plt.figure(figsize=(7,6))
sns.regplot(df,x = df["bmi"], y=df["disease_progression"])
Out[18]:
<Axes: xlabel='bmi', ylabel='disease_progression'>

Now using the Linear Regression model as the data are in continuous¶

In [19]:
x = df.iloc[:,:-1]
x
Out[19]:
age sex bmi bp s1 s2 s3 s4 s5 s6
0 0.038076 0.050680 0.061696 0.021872 -0.044223 -0.034821 -0.043401 -0.002592 0.019907 -0.017646
1 -0.001882 -0.044642 -0.051474 -0.026328 -0.008449 -0.019163 0.074412 -0.039493 -0.068332 -0.092204
2 0.085299 0.050680 0.044451 -0.005670 -0.045599 -0.034194 -0.032356 -0.002592 0.002861 -0.025930
3 -0.089063 -0.044642 -0.011595 -0.036656 0.012191 0.024991 -0.036038 0.034309 0.022688 -0.009362
4 0.005383 -0.044642 -0.036385 0.021872 0.003935 0.015596 0.008142 -0.002592 -0.031988 -0.046641
... ... ... ... ... ... ... ... ... ... ...
437 0.041708 0.050680 0.019662 0.059744 -0.005697 -0.002566 -0.028674 -0.002592 0.031193 0.007207
438 -0.005515 0.050680 -0.015906 -0.067642 0.049341 0.079165 -0.028674 0.034309 -0.018114 0.044485
439 0.041708 0.050680 -0.015906 0.017293 -0.037344 -0.013840 -0.024993 -0.011080 -0.046883 0.015491
440 -0.045472 -0.044642 0.039062 0.001215 0.016318 0.015283 -0.028674 0.026560 0.044529 -0.025930
441 -0.045472 -0.044642 -0.073030 -0.081413 0.083740 0.027809 0.173816 -0.039493 -0.004222 0.003064

442 rows × 10 columns

In [20]:
y = df["disease_progression"]
y
Out[20]:
0      151.0
1       75.0
2      141.0
3      206.0
4      135.0
       ...  
437    178.0
438    104.0
439    132.0
440    220.0
441     57.0
Name: disease_progression, Length: 442, dtype: float64

Now spiliting the data into training and test data¶

In [21]:
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn import linear_model
from sklearn import metrics
x_train,x_test,y_train,y_test = train_test_split(x,y,test_size = 0.2,random_state = 1)

Using linear model¶

In [22]:
regres = LinearRegression().fit(x_train,y_train)

Doing some prediction¶

In [23]:
y_test_pred = regres.predict(x_test)

working with some metrics to find slope, intercept and score of train and test dataset¶

In [24]:
print(" The intercept is ", regres.intercept_)
print("The  slope is ", regres.coef_)

 The intercept is  151.4300932966009
The  slope is  [ -30.62219046 -272.2506057   528.85252681  327.69716891 -581.01973841
  332.97061365  -27.97314298  139.28036115  665.07667773   61.90517166]
In [25]:
print("The score of train data set ", regres.score(x_train,y_train)*100)
print("The score of test data set ", regres.score(x_test,y_test)*100)

The score of train data set  53.32283636912148
The score of test data set  43.8431621336928

finding the loss on the train and test dataset¶

In [26]:
print(" Mean Absloute Error ",metrics.mean_absolute_error(y_test,y_test_pred))
print("Mean Square Error ",metrics.mean_squared_error(y_test,y_test_pred))

 Mean Absloute Error  41.97492114949366
Mean Square Error  2992.5812293010163
In [27]:
plt.figure(figsize=(8, 8))
plt.scatter(y_test, y_test_pred)
plt.plot(y_test, y_test, color='r')
plt.title('Actual VS Predicted Values (TEST SET)')
plt.xlabel('Actaul Values')
plt.ylabel('Predicted Values')
plt.show()

Obersation from data set :¶

-) Training data is dispersed too much, BMI vs Disease Progression has normal corelation so I think linear regression is not that good for this model.¶

-) Also from loss function we can see that we have high Mean Absloute Error which means the model is not functioning effectively and the forecasts are far from the actual values, according to a high MAE.¶